Design Charts for Seismic Analysis of Pile Groups

Design Charts for Seismic Analysis of Pile Groups

Moinuddin Ahmed

Professor, Dept. of Civil Engineering, Muffakham Jah College of Engg.& Tech. , Hyderabad.

D. Babu Rao

Formerly Professor, Dept. of Civil Engineering, Osmania University, Hyderabad.

ABSTRACT -: In the seismic analysis of pile groups an important parameter is the frequency of pile group system. Non- dimensional design curves and tables are developed for seismic analysis of long piles for different configurations of pile group.

pile-structure system. The frequency depends on stiffness of soil, pile and pile-soil-pile interaction. The behaviour of a single pile based on the concept of 'Beam on an elastic

foundation' is given by

These curves are formulated for spacing of 2d, 4d and 6d, and are useful in estimating the period of vibration of the pile-soil system. The formulation is based on the stiffness of pile group system computed from the stiffness of individual piles, accounting interaction effects. An illustration is presented herein to highlight the application of design curves for seismic analysis of pile supported structures.

KEY WORDS -: seismic, pile, soil, pile stiffness, group stiffness.

E I (d 4 y / dx4 ) K y 0

p p s

y = displacement of pile

Ep = modulus of Elasticity of pile material Ip = moment of inertia of pile cross section d = diameter (or) width of pile

Ks = Kh.d

(1)

1. INTRODUCTION

Pile foundations are essential when heavy structures are to be

Ks and Kh both represent soil modulus in N/mm2 and N/mm3 respectively.

The horizontal stiffness of long pile with pile head fixed is obtained from the solution of the above equation.

supported by weak soils. In addition to vertical loads, piles are encountered by lateral loads due to wind, sea-waves, and

Stiffness of pile K

4 3E I

(2)

p p p

earthquakes. Seismic resistant design of pile groups is a

complex problem due to the uncertainties involved in it. Poulos (1971 a & b) presented an analysis for laterally loaded

Where

Ks / 4Ep I p

piles and pile groups where in the interaction between two identical vertical piles subjected to horizontal load and moment is analyzed and then extended to pile groups. Prakash and Puri (1993) presented a method for seismic analysis of single pile wherein they developed two sets of non- dimensional frequency curves for cohesive and cohesionless soils. Extensive parametric studies by Novak M and El- Sharnouby (1984) concluded that static interaction factor approach is also accurate for dynamic analysis if the frequency range is low, as in case of earthquakes.

Seismic behaviour of pile groups depends on soil characteristics, pile properties and spacing of piles in a group.

The interaction effect of piles can be incorporated by using interaction factors for the piles in a group. The horizontal interaction factor mainly depends on soil characteristics, pile properties and spacing of piles. The interaction factors developed by Poulos (1971b) for static lateral loads are sufficiently accurate for dynamic loads if the frequency range is low. The frequency range for earthquakes is usually low. Hence, static interaction approach can be used for seismic analysis. Based on interaction factor concept the stiffness of pile group can be computed from Equation (3), Moinuddin Ahmed & Babu Rao (2005).

K

4 3E I

The seismic resistant design of pile group involves assessment of lateral load capacity and stiffness of the pile group system.

Pile Group Stiffness

g

p p

h

(3)

The lateral load behaviour of a pile depends on whether it behaves as a long flexible pile or a short rigid pile (IS:2911). An attempt has been made to develop design curves and charts for different configurations of pile groups to permit the design of pile groups for seismic loading conditions. In the present study, long piles in a group are analyzed.

2 MATHEMATICAL MODEL

In the seismic analysis of structures supported on pile foundations an important parameter is the frequency of soil-

n = No. of piles in a group

h = Group Interaction Factor Equation (3) can be rewritten as

K 1 n K L

h

g L s

Kg f .Ks .L

L = Length of pile

Group stiffness parameter

f 1 n

L h

(4)

Table No. 2 – Group stiffness parameter ffor 3 x 3 pile group

The group stiffness parameter f can be computed from design curves. This parameter f is a function of interaction factors, number of piles and the spacing of piles in a group. Using the value of f and the weight acting over the pile cap, the period of the vibration of the group can be determined.

Period of Vibration T 2

W / g. f .Ks .L

(5)

For the validation of the mathematical model experimental tests were conducted for pile groups, Moinuddin Ahmed & Babu Rao (2005).

1. DESIGN CHARTS

   Using Equation (4), design charts (Table 1 4) were developed for Group stiffness parameter f for different values of pile-soil stiffness factor L.

   Table No. 1 – Group stiffness parameter f for 2 x 2 pile group

   Table No. 3 – Group stiffness parameter f for 4 x 4 pile group

   L	s/d = 2	S/d = 4	s/d = 6
   1	1.580	2.020	2.270
   2	0.790	1.010	1.135
   3	0.527	0.673	0.756
   4	0.395	0.505	0.567
   5	0.316	0.404	0.454
   6	0.263	0.336	0.378
   7	0.226	0.288	0.324
   8	0.197	0.252	0.284
   9	0.175	0.224	0.252
   10	0.158	0.202	0.227
   11	0.144	0.184	0.206
   12	0.132	0.168	0.189
   13	0.121	0.155	0.175
   14	0.113	0.144	0.162
   15	0.105	0.135	0.151
   16	0.099	0.126	0.142
   17	0.093	0.119	0.134
   18	0.088	0.112	0.126
   19	0.083	0.106	0.119
   20	0.079	0.101	0.114
   21	0.075	0.096	0.108
   22	0.072	0.092	0.103
   23	0.069	0.088	0.099
   24	0.066	0.084	0.095

   L	s/d = 2	S/d = 4	s/d = 6
   1	2.700	3.850	4.660
   2	1.350	1.925	2.330
   3	0.900	1.283	1.553
   4	0.675	0.962	1.165
   5	0.540	0.770	0.932
   6	0.450	0.642	0.777
   7	0.386	0.550	0.666
   8	0.337	0.481	0.583
   9	0.300	0.428	0.518
   10	0.270	0.385	0.466
   11	0.245	0.350	0.424
   12	0.225	0.320	0.388
   13	0.208	0.296	0.358
   14	0.193	0.275	0.333
   15	0.180	0.257	0.311
   16	0.169	0.241	0.291
   17	0.159	0.226	0.274
   18	0.150	0.214	0.259
   19	0.142	0.203	0.245
   20	0.135	0.192	0.233
   21	0.129	0.183	0.222
   22	0.123	0.175	0.212
   23	0.117	0.167	0.203
   24	0.112	0.160	0.194

   Table No. 4 – Group stiffness parameter f for 4 x 6 pile group

   L	s/d = 2	s/d = 4	s/d = 6
   1	3.320	4.820	5.925
   2	1.660	2.410	2.963
   3	1.107	1.607	1.975
   4	0.830	1.205	1.481
   5	0.664	0.964	1.185
   6	0.553	0.803	0.988
   7	0.474	0.689	0.846
   8	0.415	0.603	0.741
   9	0.369	0.536	0.658
   10	0.332	0.482	0.593
   11	0.302	0.438	0.539
   12	0.277	0.402	0.494
   13	0.255	0.371	0.456
   14	0.237	0.344	0.423
   15	0.221	0.321	0.395
   16	0.208	0.301	0.370
   17	0.195	0.284	0.349
   18	0.184	0.268	0.329
   19	0.175	0.254	0.312
   20	0.166	0.241	0.296
   21	0.158	0.230	0.282
   22	0.151	0.219	0.269
   23	0.144	0.210	0.258
   24	0.138	0.201	0.247

2. PILE CAP DISPLACEMENT

   Spectral acceleration co-efficient for the known period of

3. APPLICATION OF DESIGN CHARTS

   The design charts are useful in the computation of period of vibration of pile groups. These charts are developed for three different spacing of piles namely 2d, 4d and 6d. These spacing are adopted because they are commonly used in practice and recommended by IS:2911 and also other International codes. However for intermediate values of s/d, group stiffness parameter can be obtained by interpolation. A typical example is presented herein to illustrate the application of design charts.

   5.1 Example

   For the seismic analysis of a 4 x 4 concrete pile group, the following information is available.

   Pile diameter=750 mm.

   Soil Modulus = 75000 KN/m3 Pile Length = 10 m

   Pile spacing to diameter ratio = 4 Weight on pile cap = 12,000 KN

   Modulus of Elasticity of pile material =0.20 X 108 kN/m2 Importance Factor=1.5

   Response Reduction Factor=4.0

   Compute Pile cap displacement for the pile group.

   Moment of Inertia of pile Ip = d4/64 = (0.75)4/64 = 0.1553 104 m4

   Ks = Kh x d = 75000 x 0.75 = 56250 KN/m2

   vibration can be evaluated by using equations givenin IS 1893-2002, based on the type of soil. The pile cap displacement can then be calculated by using Spectral

   4 Ks

   4Ep I p

   = 0.4612 m1

   acceleration co-efficient Sa/g and pile group stiffness, according to the seismic zone of the site, Importance Factor and Response Reduction Factor.

   Horizontal Seismic force (Q) = Design Seismic coefficient x Weight of structure

   L = 4.61

   Using design charts, f = 0.835

   Period of vibration of the group is given by

   Q = Ah x W (IS: 1893-2002)

   T 2

   W

   g. f .Ks .L

   where

   A Z I Sa h 2 R g

   T = 0.32 Sec

   For medium soil Sa/g = 2.5 (As per IS: 1893 2002) I = 1.5, R = 4.0

   Q Z I Sa W

   2 R g

   For Zone IV, Z = 0.24

   W S Z I

   Pile cap displacement a

   Pile cap displacement () = Q/Kg

   f .Ks L R 2 R

   Z I Sa W

   2 R g Kg

   (6)

   = 2.874 x 103 m (or) 2.874 mm

   Substituting Kg, Equation (6) can be re-written as

   W Sa Z I f .Ks L R 2 R

   (6.1)

4. CONCLUSIONS

1. Seismic response of pile group depends on type of soil, pile, diameter, modulus of elasticity of pile material and pile spacing.

2. Rational evaluation of soil modulus is essential for proper estimation of pile stiffness since the frequency of pile group largely depends on the stiffness of piles.

3. It is observed from design charts that the Group Stiffness parameter f decreases with increase in pile soil stiffness factor L and the parameter f has insignificant change at higher values of L.

   REFERENCES

   1. IS: 1893-2002 Criteria for Earthquake Resistant Design of structures Part I.

   2. Moinuddin Ahmed and Babu Rao, D (2005) Seismic response of long piles in a group: – Proc. of National Conference on Geotechics in Environmental Protection, Allahabad.

   3. Novak, M and El-Sharnouby, B (1984). Evaluation of dynamic experiments on pile group. Jl. of Geotechnical Engineering Division, ASCE, Vol 110, No. GT 6, pp: 738-756.

   4. Poulos, H.G. (1971a). Behaviour of Laterally Loaded Piles: I Single Piles, Jl. of Soil Mechanics and Foundation Division, Proc. ASCE, 97 SM-5, 711-731.

   5. Poulos, H.G. (1971b). Behavior of laterally loaded piles-II-pile groups:, Jl. of Soil Mechanics and Foundation Division, Proc. ASCE, 97 SM-5, 711-731.

   6. Prakash, S; SreeRama, K; Vijay, K.P. (1993) Dynamic pile- Soil-Pile interactions, Proceedings of the seminar on Soil Dynamics and Geotechnical Earthquake Engineering. Balkama/Rotterdam/Brookfield, pp: 353-386